Question

The solution to this equation is incorrect. Determine the error.

x - 78 = -42

A) x = 78 - 42
B) x = -36
C) x = 120
D) x = -120

Answer 1

The student's solution is incorrect because they might have subtracted instead of added during the step to isolate x, leading to the incorrect result x = -36 when it should be x = 36.

Step-by-step explanation:

The correct way to solve the equation x - 78 = -42 is to isolate the variable x by adding 78 to both sides of the equation. This gives us:

• x - 78 + 78 = -42 + 78
• x = 36

Therefore, the correct answer is x = 36, which means option B) x = -36 is clearly incorrect. The student might have subtracted 42 from 78 instead of adding them, leading to the incorrect solution of 88 which is not listed among the provided options. This can be a common mistake when dealing with negative numbers.

The error in option B)

Option B is incorrect because it shows a negative result for x, whereas the correct computation leads to a positive result. By adding the numbers incorrectly, the student might have arrived at the wrong sign for their answer.